OT: off-topic

[Huaiyu Zhu]

Andrew Dalke <dalke at dalkescientific.com> wrote:
>Tim Golden:
>> Isn't this similar to (someone-or-other's) proof that there's no such
>thing
>> as an uninteresting number?
>  ...
>> However, the smallest number in this list is the smallest uninteresting
>> number, and is therefore interesting, so it moves to the list of
>interesting
>> numbers, leaving you with the smallest remaining uninteresting number,
>which
>> therefore becomes interesting, etc. etc.
>
>Since we're off-topic...
>
>I heard this years ago.  I've thought about it, and decided that the
>proof depends on the concept of "sort" since there needs to be a "smallest."
>Are there interesting vs. non-interesting sorts?  Sorts are just numbers,
>after all.
>
>Plus, all it really says is "interesting" doen't have a closed cover.
>The values of interesting can approach but never be 0 ("uninteresting")
>and for any positive value of "interesting" you can always find a
>number which is less interesting than that.

If real numbers are allowed in addition to 0 and 1 as membership values,
most of these paradoxes can be solved.  For example the liar's paradox has a
truth value p that satisfies

	p == 1 - p,

its solution being p = 1/2.  Quite sensible, isn't it?  But more general
calculus along this direction has to be in the framework of probability
rather than fuzzy logic, of course.


Huaiyu